This book comprehensively describes recent developments in the research of renormalizable quantum gravity, focusing on its application to physics beyond the Planck scale, particularly in inflationary cosmology. It challenges the notion that the Planck scale is an impassable barrier, addressing issues such as singularity, renormalizability, unitarity, time, primordial fluctuations, and the cosmological constant. To describe the trans-Planckian world, it is necessary to break away from the view of graviton scattering and carry out the quantization of spacetime itself. Utilizing conformal field theory techniques to achieve background freedom, the book presents a renormalizable quantum theory of gravity that overcomes the Planck-scale wall.

Historically, discussions on renormalizability of gravity declined due to ghost issues. However, ghosts are essential in gravitational systems where the total Hamiltonian/momentum vanishes strictly, for aspects such as cosmic entropy, the formation of the universe, and gravitational objects. Quantum gravity approaches known in recent years often break diffeomorphism invariance or sacrifice renormalizability to eliminate ghosts. In contrast, this book presents a novel attempt which maintains that these are guiding principles even in the trans-Planckian domain, but constrains ghosts to be unphysical. The renormalizability implies a new scale that leads to a quantum gravity inflation scenario with a spacetime phase transition as the Big Bang. This book offers fresh insights into the trans-Planckian physics for graduate students and researchers.

Provides a comprehensive description of trans-Planckian physics with renormalizable quantum gravity Reveals the physical meaning of background-free nature in quantum gravity states with BRST conformal invariance Includes an inflation scenario driven solely by quantum gravity effects without introducing an unknown scalar field

Autorentext

Ken-ji Hamada is a faculty member of the Theory Center at the High Energy Accelerator Research Organization (KEK). He received his PhD in physics from Hiroshima University in 1989. He has worked on string theory, conformal field theory, and quantum gravity in two dimensions, and then proposed and developed a novel approach to renormalizable quantum gravity based on conformal field theory. Further, he recently has focused on the applications of his quantum gravity theory to trans-Planckian physics.

Inhalt

Preface.- What quantum gravity should reveal.- Renormalizable quantum gravity.- Conformal invariance as background freedom.- Physical meaning of Hamiltonian constraint.- Renormalization by dimensional regularization.- BRST conformal algebra and physical states.- Quantum gravity inflation.- Localized massive excitation of quantum gravity.- What the cosmological constant problem is.- Amplitude reduction of fluctuations and primordial spectra.- Topology and quantum gravity.- Simplicial quantum gravity.